Chapter VII
Comparing Sizes
Comparing sizes
The chapter "Comparing Sizes" introduces children to the fascinating world of observing, analyzing, and ordering the objects around them by size. It is through play with blocks - cylinders, gears, and platforms, stacking them and joining them - that children learn to notice and compare sizes: long - short, tall - short, big - small, bigger - smaller, thicker - thinner.
In the suggested games, preschool children handle concrete objects, arrange them in order, create constructions, and also make their first attempts at classifying and measuring "by eye" and with simple references (e.g. their own hand or the number of pieces). In this way they develop mathematical skills in a natural, sensory, engaging way - through action, building, and experimenting.
These games are an important stage preparing children for later mathematical skills - such as measuring, estimating, counting, and analyzing relations between sizes. Work with blocks lets them experience these ideas in a practical, tangible way, which is extremely important at the preschool stage.
After completing the set of games and tasks from this chapter, the child:
- Recognizes and names basic ideas related to size, such as: big-small, bigger-smaller, tall-short, long-short, wide-narrow.
- Compares two or more objects by size, describing the differences in words ("This one is taller", "That one is smaller").
- Arranges objects in order according to one feature (e.g. from largest to smallest, from shortest to longest).
- Matches pieces into pairs of the same size (e.g. two identical gears).
- Experiments with building constructions of different heights, lengths, and widths, analyzing their size based on the number of blocks used.
- Makes simple comparative measurements - e.g. checks which tower is taller, which bridge is longer, which cylinder rolls farther.
- Uses mathematical words in everyday speech during play (e.g. "my path is longer", "this gear is bigger").
- Understands the relation between size and function (e.g. a shorter bridge does not reach the end of the table).
- Develops spatial orientation and logical thinking by constructing and analyzing differences in buildings.
- Cooperates with classmates while doing the tasks, sharing materials and comparing the results of the work together.
Small, Bigger, Biggest Gear
Learning goal
Developing the skill of comparing the sizes of pieces.
Needed elements
Gears, platforms, cylinders, straight connectors.
How it goes
Children receive one piece of each kind of block (a connector, a cylinder, a gear, a platform). They arrange them from smallest to largest. They name them and compare: "This one is bigger/smaller than...".
Variants
Close your eyes and recognize the size of a gear by touch only.
Cylinder Towers - Who Will Build a Taller One?
Learning goal
Comparing the heights of constructions.
Needed elements
Cylinders, platforms, connectors.
How it goes
Children build towers from cylinders and connectors and place them on platforms. They compare: "Whose tower is taller?", "Which one is shorter?" They measure the towers with a hand or a ruler.
Variants
Build a tower with your eyes closed, counting the cylinders and connectors.
Who Has the Bigger Block
Learning goal
Comparing and pointing out differences.
Needed elements
Gears, connectors, cylinders, platforms, bags.
How it goes
Two children each draw one block from a bag.
They compare: "Which one is bigger?", "Which one is smaller?"
Variants
Children draw two pieces each, place them side by side, edge to edge, and compare which arrangement of two blocks is longer.
Comparing the Lengths of Caterpillars
Learning goal
Comparing lengths by building and measuring.
Needed elements
Cylinders, connectors.
How it goes
Each child builds a one-color "caterpillar" from cylinders (e.g. a blue one) and connectors. We let the children build for a set length of time, e.g. 2 minutes / 5 minutes. Then they compare the lengths of the constructions.
Variants
Build two caterpillars of the same length, but from a different number of cylinders (once use straight connectors, and once cross connectors).
Join the caterpillars into one and check with the whole class how long the caterpillar is (the unit of measure may be, for example, heel-to-toe steps - tiny steps, foot to foot).
Bridges of Different Lengths
Learning goal
Recognizing differences in length and height.
Needed elements
Platforms, cylinders, cross connectors.
How it goes
Children create bridges from platforms joined with cylinders. They place them between tables. Then they compare: which is longer, which is taller.
Variants
Build a bridge that will hold the weight of a small vehicle built from blocks. Arrange the bridges on the ground, in order from shortest to longest.
Towers of Colors and Sizes
Learning goal
Classification by two features: color and size.
Needed elements
Cylinders and gears in different colors.
How it goes
Children arrange towers from gears of the same colors, some larger, some smaller (e.g. a large blue tower, a small red one, etc.). Then they compare: "Which colorful tower is the tallest?", "Which has the largest gear on top?"
Variants
Arrange the towers from the largest to the smallest gear, but change the colors.
A timed task - who can build a tower faster from the same number of blocks: one tower from gears, the other from cylinders joined with connectors.
A Length Race - the Path to the Finish
Learning goal
Spatial comparison of lengths and distances.
Needed elements
Platforms joined in a line (one next to another) or cylinders joined with connectors.
How it goes
Children build "paths" made of a smaller or larger number of blocks (given by the teacher). Then they measure the paths and compare them with others: which path is the shortest, and which is the longest.
Variants
Children join all the constructions together, trying to connect two distant points in the room with a path. They check the length of the path using elbows, heel-to-toe steps, ordinary steps, and so on.
Children build a path with turns and try to lay it out "flat" in order to compare the length.
Guess Which One Is Longer!
Learning goal
Developing the skill of estimating and comparing lengths.
Needed elements
Cylinders, connectors, gears.
How it goes
The teacher prepares several sets with different amounts:
? gears (the number chosen by the teacher),
? connectors and cylinders (both pieces in the same amount), e.g. 11 pieces in one set, 8 in another, and so on.
Children look at the sets of pieces and estimate from which group they will be able to build the tallest tower. Then they build the constructions and place them next to each other.
Variants
? Three constructions - arrange them in order of length.
? We also add a set of platforms (there may then be fewer pieces, and the tower may be taller).
Bridges over the Chasm - Who Will Build a Longer One?
Learning goal
Comparing the lengths of bridge constructions, estimating.
Needed elements
Platforms, cylinders, cross connectors, tables in the rooms.
How it goes
- The teacher divides the children into groups and places the children's tables at different distances from one another (e.g. 30 cm, 50 cm, 70 cm).
- The teacher tells the children that the spaces between the tables are a chasm - they need to build a bridge over it between two rocks (the tables).
- Each group's task is first to estimate how many blocks will be needed to build the bridge, and then to build the bridge.
- Then the children compare the lengths of the bridges they built and also check how many pieces were used to build the bridge - they compare this with their estimates.
Variants
? The bridge must be stable, so that a vehicle made of blocks can drive across it.
? Build two bridges: one from short connectors, the other from long ones - compare which required more pieces.
Block Order - Arrange from Smallest to Largest
Learning goal
Ordering pieces by size.
Needed elements
Gears, cylinders, platforms, straight connectors and cross connectors, cranks.
How it goes
Children receive a set of 5 pieces of different sizes. They arrange them in order from smallest to largest / shortest to tallest.
Variants
The teacher decides how the particular pieces are placed (e.g. a gear may lie flat or stand vertically).
Do the reverse ordering - from largest to smallest.
Platform Stairs
Learning goal
Building a stepped construction - comparing heights.
Needed elements
Platforms, cylinders (different numbers).
How it goes
Using cylinders and cross connectors, children in groups build stairs. Then they compare: "Which step is the highest?", "Which is the lowest?"
Variants
A figure walks up the stairs and counts the steps. It may also walk down (we count down).
We add conditions for building the construction - e.g. the first step is blue, the fourth and sixth are red.
Small Ones Inside, Large Ones Outside
Learning goal
Constructing with different sizes - positioning by size.
Needed elements
Blocks.
How it goes
Children build a large circle together, arranging cylinders on the carpet, one next to another. Then inside they build a square from gears, inside that they place e.g. a triangle built from connectors, and still further inside e.g. a square or rectangle from platforms.
Then the children discuss with the teacher:
? which shape is the largest, which is the smallest?
? from how many blocks are the particular shapes built?
? from which colors? how many blocks in each color?
Variants
The teacher changes the challenge, e.g. inside a large circle of gears build two rectangles from cylinders. In one of the rectangles we build a circle from connectors, and in the other a square from four platforms.